A point O is taken inside an equilateral ΔABC. If OL BC, OM AC and ON AB such that OL = 14 cm, OM = 10 cm and ON = 6 cm, find the area of ABC.

Question

Philoid · Accepted Answer

Let each side of be a cm

So, area () = Area () + Area () + Area ()

On taking “a” as common, we get,

= 15a cm² (i)

As, triangle ABC is an equilateral triangle and we know that:

Area of equilateral triangle = cm² (ii)

Now, from (i) and (ii) we get:

15a =

15 × 4 =

60 =

a =

a = 20√3 cm

Now, putting the value of a in (i), we get

Area () = 15 × 20√3

= 300√3 cm²